Ionic Coordination and Silicate Structures Lecture 4

Elemental Abundance in Crust Element % by wt mol wt mol wt % by mol O Si Al Fe Ca Na K Mg

Elemental Abundance in Crust Element Ionic Radius (R) R/R Oxygen O Si Al / /0.42 Mg Fe Fe Ca / /0.86 Na / /0.89 K / /1.24 C

Atoms and Ions Have Different Radii

Pauling’s Rules RULE 1: Around every cation, a coordination polyhedron of anions forms, in which the cation-anion distance is determined by the radius sums and the coordination number is determined by the radius ratio. RULE 1: Around every cation, a coordination polyhedron of anions forms, in which the cation-anion distance is determined by the radius sums and the coordination number is determined by the radius ratio.

Cation-Anion Distance (Ionic)

Covalent Radius IS Smaller than Ionic Radius

Coordination Number Coordination number (c.n.) is the sum of the total number of neighbors of a central atom in a compound Coordination number (c.n.) is the sum of the total number of neighbors of a central atom in a compound Controlled by the ratio of radii of the ions Controlled by the ratio of radii of the ions What arrangement of ions of a given size will allow them to be the most closely packed? What arrangement of ions of a given size will allow them to be the most closely packed? Coordination number affects ionic radii Coordination number affects ionic radii Larger CN results in larger ionic radius Larger CN results in larger ionic radius

CN=2: Linear Not important in minerals Not important in minerals Carbon Dioxide

CN=3: Triangular

CN=4: Tetrahedral

CN=6: Octahedral

CN=8: Cubic

CN=12: Hexagonal or Cubic Close Packed

Coordination of Common Crustal Ions Element R/R Oxygen CN Coordination with O Si Tetrahedral Al /0.424/6Tetrahedral/Octahedral Mg Octahedral Fe Octahedral Fe Octahedral Ca /0.866/8Octahedral/Cubic Na /0.896/8Octahedral/Cubic K /1.248/12Cubic/Closest

General Formula for Silicates Ions in silicates will be in tetrahedral, octahedral, or cubic/closest packed coordination Ions in silicates will be in tetrahedral, octahedral, or cubic/closest packed coordination General Formula: General Formula: X m Y n (Z p O q ) W r X = 8-12 CN X = 8-12 CN Y = 6 CN Y = 6 CN Z = 4 CN Z = 4 CN O = Oxygen O = Oxygen W = OH, F, Cl W = OH, F, Cl SiteCNIons Z4 Si 4+, Al 3+ Y6 Al 3+, Fe 3+, Fe 2+, Mg 2+, Mn 2+, Ti 2+ X8 Na +, Ca K +, Ba 2+, Rb +

Mineral Formula Examples General Formula General Formula X m Y n (Z p O q ) W r Augite (Ca,Na)(Mg,Fe,Al,Ti)(Si,Al) 2 O 6 Augite (Ca,Na)(Mg,Fe,Al,Ti)(Si,Al) 2 O 6 Muscovite KAl 2 (Si 3 Al)O 10 (OH,F) 2 Muscovite KAl 2 (Si 3 Al)O 10 (OH,F) 2 Plagioclase (Na,Ca)(Si,Al) 4 O 8 Plagioclase (Na,Ca)(Si,Al) 4 O 8

Pauling’s Rules RULE 2: Ionic Bond Strength An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an ion equal the charge on that ion. RULE 2: Ionic Bond Strength An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an ion equal the charge on that ion. Electrostatic Valency = Cation Charge/CN Electrostatic Valency = Cation Charge/CN Measure of bond strength Measure of bond strength

Requirements of Rules 1 and 2 Stable coordination numbers for Si and Al result in complex ions Stable coordination numbers for Si and Al result in complex ions Si tetrahedra and Al octahedra must bond with other ions to balance negative charge Si tetrahedra and Al octahedra must bond with other ions to balance negative charge Insufficient cations to balance negative charge Insufficient cations to balance negative charge Tetrahedra and octahedra must commonly share oxygens with other complex ions Tetrahedra and octahedra must commonly share oxygens with other complex ions

Pauling’s Rules RULE 3: Shared edges, and particularly faces of two anion polyhedra in a crystal structure decreases its stability. RULE 3: Shared edges, and particularly faces of two anion polyhedra in a crystal structure decreases its stability. Maximizes distance between cations, and therefore minimizes repulsion Maximizes distance between cations, and therefore minimizes repulsion

Requirements of Rule 3 In silicates the tetrahedra will share oxygens with neighboring tetrahedra, as well as with neighboring octahedra In silicates the tetrahedra will share oxygens with neighboring tetrahedra, as well as with neighboring octahedra

Pauling’s Rules RULE 4: In a crystal structure containing several cations, those of high valency and small coordination number tend not to share polyhedral elements. RULE 4: In a crystal structure containing several cations, those of high valency and small coordination number tend not to share polyhedral elements. A follow-up to Rule 3 A follow-up to Rule 3

Requirements of Rules 3 and 4 Si 4+ has a high valency and low coordination number (4 with oxygen), so silica tetrahedra will not share sides or faces Si 4+ has a high valency and low coordination number (4 with oxygen), so silica tetrahedra will not share sides or faces Arrangements of silica tetrahedra must be based on the sharing of apices Arrangements of silica tetrahedra must be based on the sharing of apices

Isolated Tetraheda Silicates (Nesosilicates) Tetrahedra do not share any oxygens with neighboring silicon ions Tetrahedra do not share any oxygens with neighboring silicon ions Charge balance achieved by bonding with cations Charge balance achieved by bonding with cations e.g., Olivine, Garnet, Kyanite e.g., Olivine, Garnet, Kyanite

Paired Silicates (Sorosilicates) Pairs of tetrahedra share one oxygen Pairs of tetrahedra share one oxygen Remaining charge balance achieved by bonding with cations Remaining charge balance achieved by bonding with cations e.g., Epidote e.g., Epidote

Ring Silicates (Cyclosilicates) Sets of tetrahedra share two oxygens to form a ring Sets of tetrahedra share two oxygens to form a ring Remaining charge balance achieved by bonding with cations Remaining charge balance achieved by bonding with cations e.g., tourmaline, beryl e.g., tourmaline, beryl

Single-Chain Silicates (Inosilicates) Sets of tetrahedra share two oxygens to form a chain Sets of tetrahedra share two oxygens to form a chain Remaining charge balance achieved by bonding with cations Remaining charge balance achieved by bonding with cations e.g., pyroxenes e.g., pyroxenes

Double-Chain Silicates (Inosilicates) Sets of tetrahedra share oxygens (2 and 3 alternation) to form a chain Sets of tetrahedra share oxygens (2 and 3 alternation) to form a chain Remaining charge balance achieved by bonding with cations Remaining charge balance achieved by bonding with cations e.g., amphiboles e.g., amphiboles

Sheet Silicates (Phyllosilicates) Sets of tetrahedra share three oxygens to form a sheet Sets of tetrahedra share three oxygens to form a sheet Remaining charge balance achieved by bonding with cations Remaining charge balance achieved by bonding with cations e.g., micas e.g., micas

Framework Silicates (Tectosilicates) Sets of tetrahedra share all 4 oxygens in 3 dimensions to form a 3-D network Sets of tetrahedra share all 4 oxygens in 3 dimensions to form a 3-D network If all tetrahedra are cored by silicon then there is no charge imbalance If all tetrahedra are cored by silicon then there is no charge imbalance e.g., quartz e.g., quartz If some tetrahedra are cored by Al, then the remaining charge balance achieved by bonding with cations If some tetrahedra are cored by Al, then the remaining charge balance achieved by bonding with cations e.g., feldspars e.g., feldspars

Silicon Content of Silicates STRUCTURE EXAMPLE FORMULA Si:O Ratio Nesosilicates Mg 2 SiO 4 1:4 Sorosilicates Zn 4 (OH) 2 Si 2 O 7.H 2 O 1:3.5 Cyclosilicates Al 2 Be 3 Si 6 O 18 1:3 Inosilicates (Single Chain) CaMgSi 2 O 6 1:3 Inosilicates (Double Chain) Ca 2 Mg 2 (Si 4 O 11 )OH 2 1:2.75 Phyllosilicates Al 2 Si 4 O 10 (OH) 2 1:2.5 TectosilicatesSiO21:2